| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam on point of tilting |
| Difficulty | Standard +0.8 This is a multi-part mechanics problem requiring calculation of center of mass for composite bodies, moments about a pivot, and geometric reasoning. Part (i) is straightforward moment equilibrium (3 marks), but part (ii) requires finding the combined center of mass of two bodies with different densities and dimensions, then using geometry to find the angle (8 marks). The problem involves more steps and spatial reasoning than typical M2 questions, but uses standard techniques without requiring novel insight. |
| Spec | 6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
\includegraphics{figure_7}
A barrier is modelled as a uniform rectangular plank of wood, $ABCD$, rigidly joined to a uniform square metal plate, $DEFG$. The plank of wood has mass 50 kg and dimensions 4.0 m by 0.25 m. The metal plate has mass 80 kg and side 0.5 m. The plank and plate are joined in such a way that $CDE$ is a straight line (see diagram). The barrier is smoothly pivoted at the point $D$. In the closed position, the barrier rests on a thin post at $H$. The distance $CH$ is 0.25 m.
\begin{enumerate}[label=(\roman*)]
\item Calculate the contact force at $H$ when the barrier is in the closed position. [3]
\end{enumerate}
In the open position, the centre of mass of the barrier is vertically above $D$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Calculate the angle between $AB$ and the horizontal when the barrier is in the open position. [8]
\end{enumerate}
\hfill \mbox{\textit{OCR M2 Q7 [11]}}